We slightly improve the lower bound of Báez-Duarte, Balazard, Landreau and Saias in the Nyman-Beurling formulation of the Riemann Hypothesis as an approximation problem. We construct Hilbert space vectors which could prove useful in the context of the so-called “Hilbert-Pólya idea”. Université de NiceSophia Antipolis Laboratoire J.-A. Dieudonné Parc Valrose F-06108 Nice Cedex 02 France burnol@m...

The space of upper triangular matrices with Hilbert{Schmidt norm can be viewed as a nite dimensional analogue of the Hardy space H2 of the unit disk when one introduces the adequate notion of \point" evaluation. A bitangential interpolation problem in this setting is studied. The description of all solution in terms of Beurling{Lax representation is given.

We prove a Beurling-Helson type theorem on modulation spaces. More precisely, we show that the only C changes of variables that leave invariant the modulation spaces M(R) are affine functions on R. A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair.

In  cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewicz-Moisil algebras. In particular, strong similarity L ukasiewicz-Moisil algebras were defined. In this paper...

P h o to g ra p h s , u n le s s o th e rw is e n o te d , c o u rt e s y o f T h é rè s e M a ll ia v in . On June 3, 2010, Paul Malliavin died at the American Hospital in Paris. At the time of his death, he was four months short of his eighty-fifth birthday. Malliavin was a major mathematical figure throughout his career. He studied under Szolem Mandelbrojt, who had returned to France after W...

We improve the currently known thresholds for basisness of the family of periodically dilated p,q-sine functions. Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity. We also determine refined bounds on the Riesz constant associated with this family. These results seal mathematical gaps in the existing lit...

One dimensional boundary value problems with lumped controls are considered. Such systems can be modeled as modules over a ring of Beurling ultradistributions with compact support. This ring appears naturally from a corresponding Cauchy problem. The heat equation with different boundary conditions serves for illustration.

In this paper, we introduce a class of infinite matrices related to the Beurling algebra of periodic functions, and we show that it is an inverse-closed subalgebra of B(`w), the algebra of all bounded linear operators on the weighted sequence space `w, for any 1 ≤ q <∞ and any discrete Muckenhoupt Aq-weight w. Constructive Approximation, To appear

Interpretations of the Beurling–Lax–Halmos Theorem on invariant subspaces of the unilateral shift are explored using the language of Hilbert modules. Extensions and consequences are considered in both the one and multivariate cases with an emphasis on the classical Hardy, Bergman and Drury–Arveson spaces.